Department for Automation, Biocybernetics and Robotics

Two-layered system for movement imitation

Research activity duration: 2007 -
Research area: Automation and Intelligent Control of Robots
Activity leader: Andrej Gams
Tadej Petrič
Leon Žlajpah

Biorobotics Laboratory, EPFL, Lausanne, Switzerland


The two-layered movement imitation system in the first laer extracts the frequency of the demonstrated movement and in the second layer learns the waveform of the demonstrated signal.

Activity description

We developed a two-layered system for movement imitation, where the first layer of the system, the canonical dynamical system,  extracts the frequency of the input signal, and the second layer of the system, the output dynamical system learns and encodes the waveform of a single period. By combining the two dynamical systems into one system we can rapidly teach new trajectories to robots without any knowledge of the frequency of the demonstration signal. The system extracts and learns only one period of the demonstration signal. Furthermore, the trajectories are robust to perturbations and can be modulated to cope with a dynamic environment. The system is computationally inexpensive, works on-line for any periodic signal, requires no  additional signal processing to determine the frequency of the input signal and can be applied in parallel to multiple dimensions. Additionally, it can adapt to changes in frequency and shape, e.g. to non-stationary signals, such as hand-generated signals and human demonstrations.


The canonical dynamical system is based on adaptive frequency oscillators in a feedback loop. Adaptive frequency oscillators (AFOs) were introduced by Buchli, Righetti and Ijspeert. A learning rule is introduced to a nonlinear oscillator and the oscillator can then learn the frequency of the input signal. With a negative feedback loop the oscillator can accurately extract several frequency componetns.


We performed several drumming experiments on the HOAP-2 (perofrmed at BIRG@EPFL, now Biorobotics Laboratory) and HOAP-3 robots. We showed the ease of learning, reproducing and modulationg different trajectories, applied to the task of drumming. We performed drumming also on the Cbi robot at ATR in Japan.


modulation_video.jpg freq_modulation.jpg

Learning of different trajectories.

Performed at BIRG @EPFL (now Biorobotics Laboratory) with A.J. Ijspeert, Lausanne, 2008.

Modulation of anchor point.

Performed at BIRG @EPFL (now Biorobotics Laboratory) with A.J. Ijspeert, Lausanne, 2008.

Modulation of frequency and amplitude, 2008/09.


Slow_down_feedback_thumb.jpg cbi_vid.jpg  
Slow-down feedback, 2008/09.

Learning and executing drumming.

Performed at ATR, Kyoto, 2009.




  • Gams A., Ijspeert A., Schaal S., Lenarčič J., On-line learning and modulation of periodic movements with nonlinear dynamical systems, 2009. [More]


  • Gams A., Ude A., Prilagajanje periodičnega gibanja novim oblikam površine : robotsko brisanje mize v vsakdanjem človeškem okolju = Adapting periodic movement to new surface : robotic table wiping in everyday human environment, 2010. [More]
  • Gams A., Do M., Ude A., Asfour T., Dillmann R., On-line periodic movement and force-profile learning for adaptation to new surface, 2010. [More]
  • Gams A., Petrič T., Žlajpah L., Controlling yo-yo and gyroscopic device with nonlinear dynamic systems, 2009. [More]
  • Gams A., Degallier S., Ijspeert A., Lenarčič J., Dynamical system for learning the waveform and frequency of periodic signals -application to drumming, 2008. [More]
  • Gams A., Righetti L., Ijspeert A., Lenarčič J., A dynamical system for online learning of periodic movements of unknown waveform and frequency, 2008. [More]